You are then restricted by copyright just like with any other creation.
If I include the source code of Windows into my product, I can't simply choose to re-license it to say public domain and give it to someone else, the license that I have from Microsoft to allow me to use their code won't let me - it provides restrictions. It's just as "viral" as the GPL.
Also, "don't use my code" is not viral. If you break the MSFT license, you pay them, which is a very well-tested path in courts. The idea of forced public disclosure does not seem to be.
If the GPL license didn't exist, and instead you just relying on copyright, then that's an injunction. You have to stop using the code you "stole" and pay reparations.
In UK law, if you distribute copyright material in the course of a business you can be facing 10 years in prison and an unlimited fine.
Sure you can't get them to agree to the GPL, they could simply stop distributing and then turn up to their stint in prison and massive fine. In reality I suspect they would take the easy way out and comply with the license.
Corporations can't go to prison.
A major problem with the western world, total lack of accountability
For GPL a court could fine them the value of their company, or settle by releasing the code. A court won't but that's because the system is built to protect moneyed entities over individuals.
You could give 15% of the ownership to the aggrieved party.